Non-Fermi liquids and the Wiedemann-Franz law

TL;DR

This paper explores how non-Fermi liquid metals violate the Wiedemann-Franz law by analyzing their thermal and electrical conductivities, emphasizing the role of slow momentum relaxation and different types of almost-conserved quantities.

Contribution

It provides universal expressions for conductivity ratios in non-Fermi liquids and discusses conditions under which the Wiedemann-Franz law is violated or upheld.

Findings

Universal conductivity ratios violate Wiedemann-Franz law in non-Fermi liquids.

Different relaxation mechanisms lead to distinct transport behaviors.

Predictions for experimental outcomes in specific strongly correlated materials.

Abstract

A general discussion of the ratio of thermal and electrical conductivities in non-Fermi liquid metals is given. In metals with sharp Drude peaks, the relevant physics is correctly organized around the slow relaxation of almost-conserved momenta. While in Fermi liquids both currents and momenta relax slowly, due to the weakness of interactions among low energy excitations, in strongly interacting non-Fermi liquids typically only momenta relax slowly. It follows that the conductivities of such non-Fermi liquids are obtained within a fundamentally different kinematics to Fermi liquids. Among these strongly interacting non-Fermi liquids we distinguish cases with only one almost-conserved momentum, which we term hydrodynamic metals, and with many patchwise almost-conserved momenta. For all these cases, we obtain universal expressions for the ratio of conductivities that violate the Wiedemann-Franz law. We further discuss the case in which long-lived `cold' quasiparticles, in general with unconventional scattering rates, coexist with strongly interacting hot spots, lines or bands. For these cases, we characterize circumstances under which non-Fermi liquid transport, in particular a linear in temperature resistivity, is and is not compatible with the Wiedemann-Franz law. We suggest the likely outcome of future transport experiments on CeCoIn5, YbRh2Si2 and Sr3Ru2O7 at their critical magnetic fields.